Emergence of Generic Entanglement Structure in Doped Matchgate Circuits

Free fermionic Gaussian, a.k.a. matchgate, random circuits exhibit atypical behavior compared to generic interacting systems. They produce anomalously slow entanglement growth, characterized by diffusive scaling S(t) ∼ √t, and evolve into volume-law entangled states at late times, S ∼ N, which are highly unstable to measurements. In this talk, I will discuss how doping such circuits with non-Gaussian resources (gates) restores entanglement structures of typical dynamics. The ballistic entanglement growth S(t) ∼ t is recovered after injecting an extensive total amount of non-Gaussian gates. When the evolution is perturbed with measurements, the system exhibits a measurement-induced phase transition between an area-law and a power-law entangled phase, S ∼ N^α , with α controlled by the doping. A genuine volume-law entangled phase is recovered only when non-Gaussian gates are injected at an extensive rate. This study bridges the dynamics of free and interacting fermionic systems, identifying non-Gaussianity as a key resource driving the emergence of non-integrable behavior.